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Exponential Asymptotic Stability of Linear Ito-Volterra Equation with Damped Stochastic Perturbations

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Exponential Asymptotic Stability of Linear Ito-Volterra Equation with Damped Stochastic Perturbations
2.	Creator	Author's name, affiliation, country	John A. D. Appleby; Dublin City University, Ireland
2.	Creator	Author's name, affiliation, country	Alan Freeman; Dublin City University, Ireland
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)
4.	Description	Abstract	This paper studies the convergence rate of solutions of the linear Ito-Volterra equation $$ dX(t) = \left(AX(t) + \int_{0}^{t} K(t-s)X(s),ds\right)\,dt + \Sigma(t)\,dW(t) \tag{1} $$ where $K$ and $\Sigma$ are continuous matrix-valued functions defined on $\mathbb{R}^{+}$, and $(W(t))_{t \geq 0}$ is a finite-dimensional standard Brownian motion. It is shown that when the entries of $K$ are all of one sign on $\mathbb{R}^{+}$, that (i) the almost sure exponential convergence of the solution to zero, (ii) the $p$-th mean exponential convergence of the solution to zero (for all $p>0$), and (iii) the exponential integrability of the entries of the kernel $K$, the exponential square integrability of the entries of noise term $\Sigma$, and the uniform asymptotic stability of the solutions of the deterministic version of (1) are equivalent. The paper extends a result of Murakami which relates to the deterministic version of this problem.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2003-12-27
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/179
10.	Identifier	Digital Object Identifier	10.1214/EJP.v8-179
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 8
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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